On the oscillation of fourth-order neutral differential equations with multiple delays

This work focuses on the canonical scenario and examines the oscillatory and asymptotic features of fourth-order differential equations with numerous delays and mixed neutral terms. The Riccati methodology is employed as a useful mathematical tool to simplify the theoretical analysis and derive stringent conditions that rule out the existence of positive solutions satisfying the examined equation. By systematically combining these conditions, precise criteria ensuring the oscillation of all solutions are obtained. These findings contribute qualitatively to the scientific literature by advancing the theoretical understanding of the oscillatory behavior of such equations. Furthermore, to highlight the practical importance of the established results, two applied examples are provided to demonstrate the effectiveness of the derived criteria in handling relevant mathematical models.